Sr Spark Cpt -14 Paper

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CODE: AYYAPPA FILE NO. IIT-582/26 (03-01-2009)

NARAYANAGROUP OF EDUCATIONAL INSTITUTIONS

IIT JEE– 2009

COMMON PRACTICE TEST-14

SR-IIT-FTB & SR-SPARK

Time: 3 hours Max. Marks: 246

DATE: 05– 01 – 09

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONSA. General:

1. This booklet is your Question Paper containing 69 questions.

2. The question paper CODE is printe on the right han topcorner o! this booklet.

". #lank papers$ clipboars$ log tables$ slie rules$ calculators$cellular phones$ pagers$ an electronic gagets in any !or%are not allo&e to be carrie insie the e'a%ination hall.

(. The ans&er sheet$ a %achine)reaable Ob*ecti+e ,esponse-heet O,-/$ is pro+ie separately.

0. DO OT T3PE, 45T 7 38T5TE TE O,- O, TE#OO:ET.

B. Filling the ORS6. On the lo&er part o! the O,-$ &rite in ink$ your na%e in bo'

1$ your ,egistration o. in bo' 2 an a%e o! the Centre inbo' ". D nt !rite the"e an#!here el"e.

;. 4rite your ,egistration o. in ink$ in the bo' ( pro+ie inthe lo&er part o! the O,- an arken the appropriate bubbleUNDER each igit o! your ,egistration o. &ith a goo quality# pencil.

<. The O,- has a CODE printe on its lo&er an upper parts.9. 3ake sure the CODE on the O,- is the sa%e as that on this

booklet an put your signature in ink in bo' 0 on the O,-a!!ir%ing that you ha+e +eri!ie this.

1=. 5> TE CODE- DO OT 3TC$ -: >O, C?E O>TE #OO:ET.

C. $%e"tin aer 'r(at:11. The question paper consists o! ) art" *Part I: +athe(ati,"

Part II: Ph#"i," Part III: Che(i"tr#. Each part has (

sections.12. Se,tin I contains 6 %ultiple choice questions. Each questionhas ( choices /$ #/$ C/ an D/$ out o! &hich nl# ne i",rre,t.

1". Se,tin II contains ( %ultiple correct ans&er type questions.Each questions has ( choices /$ #/$ C/ an D/$ out o! &hich one or %ore ans&ers are correct.

1(. Se,tin III contains ( ,easoning type questions. Eachquestion contains -TTE3ET)1 D -TTE3ET)2.#ubble / i! both the state%ents are T,8E an

-TTE3ET)2 is the correct e'planation o! -TTE3ET)1.

#ubble #/ i! both the state%ents are T,8E but-TTE3ET)2 is OT the correct e'planation o! -TTE3ET)1.

#ubble C/ i! -TTE3ET)1 is T,8E an -TTE3ET)2 is>-E.

#ubble D/ i! -TTE3ET)1 is >-E an -TTE3ET)2 is

T,8E.10. Se,tin I/ contains " sets o! inke)Co%prehension type

question. Each set consists o! a paragraph !ollo&e by "questions. Each question has ( choices /$ #/$ C/ an D/$out &hich nl# ne i" ,rre,t.

D. +ar0ing S,he(e:16. >or each questions in Se,tin I$ you &ill be a!ar1e1 ) (ar0"

i! you ha+e arkene only the bubble corresponing to thecorrect ans&er an @ero %ark i! no bubble is arkene. 5n allother cases$ (in%" ne *23 (ar0 &ill be a&are.

1;. >or each question in Se,tin II$ you &ill be a!ar1e1 4 (ar0"i! you ha+e arkene all the bubbles/ corresponing to thecorrect ans&er an @ero %ark !or all other cases. 5! %ay benote that there is n negati5e (ar0ing 'r !rng an"!er.

1<. >or each quest ion in Se,tin III$ you &ill be a!ar1e1 )(ar0" i! you arken only the bubble corresponing to thecorrect ans&er an @ero %ark i! no bubble is arkene. 5n allother cases$ (in%" ne *23 (ar0 &ill be a&are.

19. >or each question in Se,tin I/$ you &ill be a!ar1e1 4(ar0" i! you arken only the bubble corresponing to thecorrect ans&er an 6er (ar0 i! no bubble is arkene. 5n allother cases$ (in%" ne *23 (ar0 !ill 7e a!ar1e1

Useful Data

Ga" Cn"tant R A <."1( B :−1 %ol−1

A =.=<21 it at% :−1 %ol−1

A 1.9<; ≈ 2 Cal :−1 %ol−1

A5ga1r8" N%(7er Na A 6.=2" × 1=2"

Plan,09" ,n"tant h A 6.620 × 1=−"( B ⋅ s 6.620 × 1= )2; erg ⋅ s

3 Fara1a# A 960== Coulo%b3 ,alrie A (.2 Boule

3 a(% 1.66 × 1= )2; kg

3 e/ 1.6 × 1= )19 B

At(i, N: A 1$ D A 1$ i A "$ a A 11$ : A 19$ ,b A ";$ Cs A 00$ > A 9$ Ca A 2=$ e A 2$ O A <$ u A ;9$ i A 2<$n A "=$ Cu A 29$ Cl A 1;$ #r A "0$ Cr A 2($ 3n A 20$ >e A 26$ - A 16$ P A 10$ C A 6$ A ;$ g A (;.

At(i, +a""e": e A ($ 3g A 2($ C A 12$ O A 16$ A 1($ P A "1$ #r A <=$ Cu A 6".0$ >e A 06$ 3n A 00$ Pb A 2=;$ u A 19;$

g A 1=<$ > A 19$ A 1$ Cl A "0.0$ -n A 11<.6$ a A 2"$ D A 2$ Cr A 02$ : A "9$ Ca A (=$ i A ;$ #e A ($ l A 2;$ - A "2.1



CODE: AYYAPPA HYD SBD ZONE / CPT-14 /

MA HEMA

CS

PART – I

SECTION – IStraight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY

ONE is correct.

. !f " #, , z z z are three distinct comple$ num%ers and a, %, c are three positi&e real num%ers

such that

" # # "

a b c

z z z z z z = =

− − − then

" " "

" # # "

a b c

z z z z z z + +

− − −

is

a) # a%c %) (a%c)# c) a ' % ' c d)

". The center of a square ABCD is at(

Z and if A is Z then centroid of ABC ∆ is

a) ( )( (" Z i Z Z − − %) ( (

"

#

Z iZ +c)

( ) ( #

#

i Z iZ − +d) (

#

Z Z −

#. um%er of wa*s, # persons ha&in+ 6 one rupee coins, one rupee coins, - one rupee coins

respecti&el* donate one rupee coin collecti&el* is .

a) "/ %) -# c) 44 d) 4

4.

(

. ."n r

n r p

r p

r p

C C −

= =

∑∑ is equal to

a) 4 # n n− + %) 4 # n n− − c) 4 # "n n− + d) 4 #n n−

0.(

tan4"

"1

a) 6 " # 4− − + + %) 6 " # 4− + − −

c) 6 " # 4− − − − d) 6 " # 4− + − +

Spac !"# #"$%& '"#




6. The num%er of solution of [ ]

sin sin sin#

y x x x = + + and [ ] "cos y y x + = where 2. 3

denotes the +reatest inte+er function is

a) 4 %) c) " d)

SECTION – II

Multiple Correct Answer TypeThis section contains 4 multiple correct answer(s) t*pe questions. Each question has 4 choices (A), (B), (C) and (D), outof which ONE OR MORE isare correct.

. !f ( ) ( )" "

"

cos tan " # sin # 4

cos x y z

x

+ + + = ÷

then

a) x can %e a multiple of π %) x cannot %e an e&en multiple of π

c) z can %e a multiple of π d) y can %e a multiple of π "

-. #

" cot , cos0

− −+ is equal to

a) 44

cot

− ÷

%) "0

cos

ec− ÷

c) 4

tan

− ÷

d) 44

cos"0

− ÷

/. !f ( )(

" " "(

( " "( " # x x a a x a x a x+ + = + + + − − − − + then

a) 6"a = %) "

"a = c) "a = d) 4

-(-0a =

. 5et ", , , nS S S − − − − − − %e the sums of +eometric series .hose st terms are , ", #, 77777,n

and common ratios are

, , , ," # 4 n

−−−−+

respecti&el*. Then

a)( )

"

#

"n

n nS S S

++ + − − − + = %) "

. nS S S n− − − − = +

c)( ) " " #

" n n

n

S S S S S S n−

−+ + − − − − =+ d)

" # 4

" #. . "4 #n

nS S S S +− − − − − =

Spac !"# #"$%& '"#




SECTION – III

Reasoning TypeThis section contains 4 reasonin+ t*pe questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY

ONE is correct.

CODE

(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct e!"a#atio# $or STATEMENT–1

(%) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct e!"a#atio# $or STATEMENT–1

(C) STATEMENT–1 is True, STATEMENT–2 is &a"se

(D) STATEMENT–1 is &a"se, STATEMENT–2 is True

. State'e#t 1 8ne side of an equilateral trian+le "4. The mid points of the sides are 9oined to

form another trian+le whose midpoints are in tern 9oined to form another trian+le and

continue the process infinite num%er times. Then sum of perimeters of all such trian+les

formed is 44.

State'e#t !f ( ) ( )" "lo+ lo+ 4a b c d + + + ≥ then the minimum &alue of a'%'c'd is -

". State'e#t 1 The coefficient of 0( x in the e$pansion of

( ) ( ) ( )(( /// //-" ((( " # x x x x x x+ + + + + + − − − + is 0(

"C

State'e#t 2 !f ( ", , , , nC C C C −−−− %e the %inomial coefficients then

( ) ( ) ( )( "

( "

n

n n

n

C C C C C C

C C C C n

−+ + −− − − − − + = + ÷− − − −

#. State'e#t 1

"

tan tan tan

# 4n n

π − − −+ + − − − − + + − − − − ∞ =+ +

Spac !"# #"$%& '"#




State'e#t 2 !f

" # 4 6

"sin .... cos

" 4 " 4 "

x x x x x x

π − −

− + + − + − − − = ÷ ÷

when " x< <

then $1

4. State'e#t 1 (

4 / # 0 0 0Cos = + + −

State'e#t 2 hen# 0

4 4 A

π π < < then sin cos

" "

A A+ < and sin cos

" "

A A− >

SECTION – IV

Linked Comprehension Type

This section contains # para+raphs. Based upon each para+raph, # multiple choice questions ha&e to %e answered. Each

question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragrah 'r $%e"tin" N". 3; t 3<

5et ( )0

0

(

r

r

r

x C x=

+ = ∑ when 0r r C C = . ow answer the followin+ questions.

0. ( 0 .r sr s C C

≤ < ≤ =∑ ∑a) "-# %) #-6 c) #/ d) "-

6. ( )"

( 0

r s

r s

C C ≤ < ≤

− =∑ ∑

a) 4-- %) " c)4 d) "-4

. ( )( 0

. r s

r s

r s C C ≤ < ≤

+ =∑ ∑

a) 4#0 %) /#0 c) /# d) 40

Paragrah 'r $%e"tin" N". 3= t >?

Spac !"# #"$%& '"#




ASSA*E +2

The cu%ic equation whose roots are" 4 -

cos ,cos ,cos

π π π is # "- 4 4 x x x+ − + = . ow

answer the followin+ questions

-. The equation whose roots are" " "" 4 -sec ,sec ,sec

π π π is

a) # ""4 - 64 u u u− + − = %) # ""4 - 64 u u u+ − + =

c) # ""4 - 64 u u u+ + + = d) # ""4 - 64 u u u− − − =

/." " " " " "" 4 - " 4 -

tan tan tan cot cot cot, , , , , ,

π π π π π π + + + + ÷ ÷

is equal to

a) - %) "4 c) -0 d) 0

"." " " " " "" " 4 " - -

sec tan sec tan sec tan

π π π π π π ÷ ÷ ÷ ÷

a) ""- %) #6- c) 44- d) /-

Paragrah 'r $%e"tin" N". >3 t >)

ASSA*E +

Consider a conic of the form ( )" "" ax hxy by+ + = − − − − and a circle

( )" "

" " "

x y

r r + = − − − − −

() :(") +i&es ( )" "

" "

" #a x hxy b y

r r

− + − = − − − − − ÷ ÷

(#) represents a pair of lines passin+ throu+h the ori+in and the intersection of the circle and

the conic. !f these lines coincide the* are with either ma9or a$is or minor a$is.

Spac !"# #"$%& '"#




(#) represent coincident lines if"

" "

a b h

r r

− − = ÷ ÷

. This is a quadratic equation interms

of "r whose roots %e"

r and

"

"r ; !f

"

r and

"

"r are %oth positi&e then the conic is an ellipse

and len+ths of its a$es are "r and ""r . !f"

r is positi&e and"

"r is ne+ati&e then the conic is

a h*per%ola and len+ths of its a$es are "r and "

"" r − . <i&en conic is

" "0 6 0 "" "6 "/ ( x xy y x y− + + − + = . The a$es %ein+ rectan+ular . ow answer the

followin+ questions.

". <i&en conic is

a) para%ola %) Ellipse

c) =*per%ola whose a$es are coordinate a$isd) =*per%ola whose a$is are not the coordinate a$es.

"" .5en+hts of ma9or and minor a$es are

a) -,4 %) 6,4 c)4," d) 6,-

"#. Equations of the ma9or and minor a$es are respecti&el*

a) " , " # x y x y+ − = − + = %) " # , " 4 x y x y− + = = + + =

c) 0 , # x y x y− + = + + = d) # , x y x y− + = + − =

PHYS CS

PART – II

SECTION – I

Straight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D),

out of whichONLY ONE is correct.

Spac !"# #"$%& '"#




"4. The amplitude of a wa&e distur%ance propa+atin+ is to positi&e $ direction is +i&en %*

"

y

x=

+ at t1 and

"

" " y

x x=

+ − at t 1" sec, where $ > * are in meter assumin+ that the

shape of wa&e distur%ance does not chan+e durin+ the propa+ation the speed of the wa&e is

a) .0ms %) ms c) .0 ms d) " ms

"0. A uniform wire of mass . ?+ and len+th ".40 m han+s from the ceilin+. @peed of the

trans&erse wa&e in the rope at a point .0 meter distance from the lower end ( )"/.- g m s=

a) "./ms %) "."ms c) #.0ms d) none

"6. The equation of a wa&e is +i&en %*"

sin#

t y

π α

= + ÷

if displacement is 0cm at t1 , then

the total phase at t 1 .0 seconds will %e

a)"

#rad

π %)

"

0 Rad

π c)

#rad

π d)

6rad

π

". A thin uniform rod of mass and len+th 5 han+s from a frictionless pi&ot and is connected

at the %ottom %* a sprin+ to the wall as shown. The sprin+ constant is . The s*stem isallowed to oscillate %* pressin+ end B of the rod and releasin+. The period of oscillation will

%e

a) " M T K

π = %) " MLT Mg KL

π =+

c)"

"6 #

MLT

KL Mg π =

+d) "

# "

MLT

KL Mg π =

+

"-. A particle is under+om+ @= with frequenc* . hat is the frequenc* of its ?inetic ener+*

a) f" %) "f c) #f d) 4f

"/. A particle of mass m performs oscillator* motion of amplitude A on the $ :a$is, a%out the

ori+in the restorin+ force on the particle is +i&en %* # F cx= − . here C is constant and $ is

the instantaneous displacement. The period of oscillation is

Spac !"# #"$%& '"#




a)!ndependent of A %) Froportional to

# A

c) Froportional to A− d) Froportional to

" A−

SECTION – II

Multiple Correct Answer Type

This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A),

(B), (C) and (D), out of whichONE OR MORE is/are correct.

#. A sprin+ %loc? s*stem under+oes @= on a smooth horiGontal surface. The %loc? is now

+i&en some positi&e chan+e , and a uniform horiGontal electric field to the ri+ht is switched

on. As a result

a) Time period of oscillation will increase %) Time period of oscillation will decrease

c) Time period of oscillation remain unaffected

d) The mean position of @= will shift to the ri+ht.

#. A coin is placed on a horiGontal platform, which under+oes &ertical simple harmonic motion

of an+ular frequenc* ω . The amplitude of oscillation is +raduall* increased. The coin will

lea&e contact with the platform for the first time

a) at the hi+hest position of the platform %) at the mean position of the platform

c) for an amplitude of

"

g ω d) for an amplitude of g ω #". A simple pendulum of len+th 5 and mass (%o%) is oscillatin+ in a plane a%out a &ertical line

%etween an+ular limits 7 φ and 'φ . or an an+ular displacement θ ( )θ φ < , the tension in

the strin+ and the &elocit* of the %o% are T and & respecti&el* . The followin+ relation hold

+ood under the a%o&e conditions

a) cosT Mg θ = %)"

cos v

T Mg M L

θ − =

c)the ma+nitude of tan+ential acceleration of %o% sinT a g θ = d) cosT Mg θ =

##. A particle of mass m is alarmed to oscillate near the minimum of nautical para%olic path" 4 x ay= the an+ular frequenc* of small oscillatin+ +i&en %*

Spac !"# #"$%& '"#




a) g

a %)

" g

ac)

"

g

ad)

#

"

g

a

SECTION – III

Reasoning Type

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D),

out of whichONLY ONEis correct.

(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct e!"a#atio# $or

STATEMENT–1

(%) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct e!"a#atio# $or

STATEMENT–1

(C) STATEMENT–1 is True, STATEMENT–2 is &a"se

(D) STATEMENT–1 is &a"se, STATEMENT–2 is True

#4. STATEMENT–I ater ?ept in a n open &essel will quic?l* e&aporate on the surface of moon

STATEMENT–II The temperature at the surface of moon is much hi+her than %oilin+ pt of

water.

#0. STATEMENT–I A %ea?er is completel* filled with water at (4 C will ne&er o&erflow, %oth

when

heated or cooled .

STATEMENT–II Densit* of water is ma$imum at (4 C

#6. STATEMENT–I !n adia%atic compression, the internal ener+* and temperature of the s*stem

+et

decreased.STATEMENT–II An e$ternal a+ent does wor? on the s*stem.

#. STATEMENT–I !nternal ener+* in an isothermal process ma* chan+e for an ideal +as.

STATEMENT–II !nternal ener+* is a function of temperature and no of moles of +as

Spac !"# #"$%& '"#



SECTION – IV

Linked Comprehension Type This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be

answered. Each question has 4 choices (A), (B), (C) and (D), out of whichONLY ONE is correct.

Paragraph for Questions Nos. 38 to 40

A wei+htless %ar is supported %* two sprin+s from a%o&e and carries a mass m suspended from a

sprin+ as shown in the fi+ure

#-. ind the time periods of small oscillations if %ar remains horiGontal e&er* time

a)( )

( ) " #

# "

m K K K T

K K K

+ +=

+ %)

( )

( ) " #

# "

""

"

m K K K T

K K K π

+ +=

+

c)( ) " # " #

" #

4"

4

m K K K K K K T

K K K π

+ += d) none of these

#/. ind the time period of small oscillations if wei+ht is equall* shared %* two upper sprin+s.

a)

( )

( )

" #

# ""

m K K K

T K K K π

+ +

= + %)

( )

( )

" #

# "

"

" "

m K K K

T K K K π

+ +

= +

c)( ) " # " #

" #

4"

4

m K K K K K K T

K K K π

+ += d) one of these

4. Accordin+ to classical mechanics time period of +i&en sprin+ mass s*stem is in&ariant

a) inertial reference frame onl* %) non inertial reference onl*

c) An* reference frame d) cant sa*

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a)"

sint

x y a t

vω

= − ÷

%)

sint

! y a t

vω

= − ÷

c) "

sint

! x ! y a t

v vω

−= − − ÷

d)

"

sint

x y a t

vω

= − ÷

46. Equation of reflected wa&e if it is reflectin+ at the 9oint and amplitude of reflected wa&e is Ra

a) ( )"sin

R y a t x vω = − %)

sin R

! ! x y a t

v vω

−= − − ÷

c)

sin R

x y a t

vω

= + ÷

d)

sin R

! x y a t

vω

+= + ÷

CHEM S RY

PART – III

SECTION – I

Straight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of

whichONLY ONE is correct.

a)

%)

c) d)

Spac !"# #"$%& '"#



a) %) c) d)

a) %) c) d)

a) %)

c) d)

Spac !"# #"$%& '"#



SECTION – IIMultiple Correct Answer Type

This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C)

and (D), out of whichONE OR MORE is/are correct.

0#. hich of the followin+ statements is trueH

a) eth*lsalic*late and Acet*lsalic*lic acid can %e distin+uished %* %oth neutral # FeC! an aq.

# "a#C$

%) BenGaldeh*de +i&es positi&e Tollens test

c) ormic acid +i&es positi&e Tollens test d) Acetophenone +i&es positi&e iadoform test

04. hich of the followin+ reactions isare not feasi%leH

a)

%) c)

d) # 4 R$# C# MgBr C# R$MgBr + → +

Spac !"# #"$%& '"#



00. Consider the followin+ compounds and sa* which of them +i&e '&e !odoform test.

a) FhC=8 %) c)# "

C# C# $# d)

06. hich of the followin+ reaction are correctl* mentionedH

a)

%)

c)

d)

Spac !"# #"$%& '"#



SECTION – III

Reasoning Type

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of

whichONLY ONEis correct.

(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct e!"a#atio# $or STATEMENT–1

(%) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct e!"a#atio# $or

STATEMENT–1(C) STATEMENT–1 is True, STATEMENT–2 is &a"se (D) STATEMENT–1 is &a"se, STATEMENT–2 is True

0. STATEMENT I " " " ".

%MF

K RC# C# Br KC" RC# C# C" KBr + → +

"

" " " "

&t$#

K RC# C# Br KC" RC# C# C" KBr + → +

!n this reaction, "

K K > . here "

> K K are the rates of reaction.

STATEMENT II D %ein+ polar aprotic sol&ent, sol&ates the K + , ma?in+ free C" − whereas in

Et8=, C" − form = : %onds with it.

0-. STATEMENT – I; cannot under+o caniGarro reaction.

STATEMENT II The lone pairs of electrons on itro+en are in&ol&ed in resonance and hence

deceases the eletrophilicit* of the car%on*l +roup.

0/. STATEMENT I The reaction with # "a#S$ of the di7t7%ut*l ?etone, is &er* slow.

STATEMENT II Due to steric effect in the ?etone .

6. STATEMENT I ehlin+s solution o$idiGes Acetaldeh*de to the acid and +i&es red ppt of "$Cu

STATEMENT II !n this reaction Cu8 acts as an o$idiGin+ a+ent .

Spac !"# #"$%& '"#



SECTION – IV

Linked Comprehension Type This section contains 4 paragraphs. Based upon each paragraph, 3 & 2 multiple choice questions have to

be answered. Each question has 4 choices (A), (B), (C) and (D), out of whichONLY ONE is correct.


ARA*RA- –I

@hown %elow is a s*nthesis of the clem%art %eetle pheromore, multistriatin.

6. The structure of B is

a) %)

c) d) All of these.

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6". The structure of D is

a) %)

c) d) one of these.

6#. The functional +roups present in D is are

a) car%on*l and c*clic ether %) alcohol and c*clic ether.

c) car%o$*lic acid onl* d) onl* car%on*l +roup


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Sr Spark Cpt -14 Paper

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